Problem: Simplify the following expression: $ r = \dfrac{1}{8} - \dfrac{6t + 4}{t + 7} $
In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{t + 7}{t + 7}$ $ \dfrac{1}{8} \times \dfrac{t + 7}{t + 7} = \dfrac{t + 7}{8t + 56} $ Multiply the second expression by $\dfrac{8}{8}$ $ \dfrac{6t + 4}{t + 7} \times \dfrac{8}{8} = \dfrac{48t + 32}{8t + 56} $ Therefore $ r = \dfrac{t + 7}{8t + 56} - \dfrac{48t + 32}{8t + 56} $ Now the expressions have the same denominator we can simply subtract the numerators: $r = \dfrac{t + 7 - (48t + 32) }{8t + 56} $ Distribute the negative sign: $r = \dfrac{t + 7 - 48t - 32}{8t + 56}$ $r = \dfrac{-47t - 25}{8t + 56}$